TY - JOUR
T1 - New formulations and convergence analysis for reduced tracer mass fragmentation model
T2 - an application to depolymerization
AU - Singh, Mehakpreet
AU - Walker, Gavin
AU - Randade, Vivek
N1 - Publisher Copyright:
© 2022 The authors. Published by EDP Sciences, SMAI.
PY - 2022/5/1
Y1 - 2022/5/1
N2 - In this work, two discrete formulations based on the finite volume approach for a reduced fragmentation model are developed. The important features such as mass conservation and accurate prediction of the zeroth order moments are accomplished by the modification of the selection function. The new schemes can compute the second order moment, which plays a significant role in predicting the area of the particles in real life applications, with high accuracy without taking any specific measures. A thorough convergence analysis of both schemes including Lipschitz condition and consistency is presented and exhibit second order convergence. The accuracy and efficiency of both schemes is demonstrated by applying them to the depolymerization problem which commonly arises in polymer sciences and chemical engineering. It is demonstrated that the new schemes are easy to implement, computationally efficient and able to compute the numerical results with higher precision even on a coarser grid.
AB - In this work, two discrete formulations based on the finite volume approach for a reduced fragmentation model are developed. The important features such as mass conservation and accurate prediction of the zeroth order moments are accomplished by the modification of the selection function. The new schemes can compute the second order moment, which plays a significant role in predicting the area of the particles in real life applications, with high accuracy without taking any specific measures. A thorough convergence analysis of both schemes including Lipschitz condition and consistency is presented and exhibit second order convergence. The accuracy and efficiency of both schemes is demonstrated by applying them to the depolymerization problem which commonly arises in polymer sciences and chemical engineering. It is demonstrated that the new schemes are easy to implement, computationally efficient and able to compute the numerical results with higher precision even on a coarser grid.
KW - Convergence analysis
KW - Depolymerization
KW - Finite volume scheme
KW - Integro-partial differential equations
KW - Reduced fragmentation model
UR - http://www.scopus.com/inward/record.url?scp=85129148669&partnerID=8YFLogxK
U2 - 10.1051/m2an/2022023
DO - 10.1051/m2an/2022023
M3 - Article
AN - SCOPUS:85129148669
SN - 2822-7840
VL - 56
SP - 943
EP - 967
JO - Mathematical Modelling and Numerical Analysis
JF - Mathematical Modelling and Numerical Analysis
IS - 3
ER -